Difference between revisions of "Vertex"

(Vertex of a parabola)
(Not every parabola is y = x^2 (if it even lives in a place with a coordinate system)!)
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==Vertex of a parabola==
 
==Vertex of a parabola==
The '''vertex''' of a [[parabola]] is the point which, if a vertical line is placed over it, divides the parabola into two equal mirror images. The vertex occurs at either the maximum value or the minimum value of the graph, depending on the coefficient of <math>x^2</math>. If it is positive, then the vertex lies at the minimum of the graph. If it is negative, then the vertex lies at the maximum of the graph.
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The '''vertex''' of a [[parabola]] is the [[midpoint]] of the [[line segment]] joining the [[focus]] of the parabola to the [[directrix]] that is perpendicular to the directrix.  This line is the line of symmetry of the parabola. If the parabola lies in a [[Cartesian coordinate system]] as the [[graph of a function | graph]] of the equation <math>y = ax^2 + bx + c</math> then this line is vertical and the vertex is the point at which the <math>y</math>-value of the graph is minimal (if <math>a > 0</math>) or maximal (if <math>a < 0</math>).
  
 
==Vertex of an angle==
 
==Vertex of an angle==

Revision as of 12:57, 7 January 2008

There are multiple uses of the word vertex in mathematics, including uses in graph theory and multiple uses in geometry.

Vertex of a parabola

The vertex of a parabola is the midpoint of the line segment joining the focus of the parabola to the directrix that is perpendicular to the directrix. This line is the line of symmetry of the parabola. If the parabola lies in a Cartesian coordinate system as the graph of the equation $y = ax^2 + bx + c$ then this line is vertical and the vertex is the point at which the $y$-value of the graph is minimal (if $a > 0$) or maximal (if $a < 0$).

Vertex of an angle

See angle.

Vertex of a polygon or polyhedron

See polygon.


Note that the plural form of the word "vertex" is the word "vertices;" the singular of "vertices" is "vertex," not "vertice."

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